Question

What is the projection of `<4,9,1 >` onto `<-1,7,2 >`?

Answer 1

`61/sqrt54`

Explanation:

`vec A={4,9,1}` and `vec B={-1,7,2}`

Projection of `vec A` on `vec B` is the dot product of `vec A` and unit vector `vec B`.

Hence;
`vec A * hat B`
`=vec A * (vec B)/(|vec B|)`
`={4,9,1}.({-1,7,2})/(sqrt(1^2+7^2+2^2))`
`=(4*(-1)+9*7+1*2)/sqrt54`
`=61/sqrt54`